Tintin is sent to guard Professor Calculus, who has invented a machine that can duplicate anything, and is staying in a village near the border of Syldavia and Bodouria. Rastapopoulous, an infamous and ruthless international criminal, tries to lure Calculus and Tintin away by kidnapping two children, who live nearby, in order to get his clutches on the machine.

Tintin falls into a dangerous trap after his friends are falsely arrested in a troubled South American country where a revolution is about to explode.

After the death of Captain Thémistocle Paparanic, Captain Haddock's old friend, he inherits a ship called the Golden Fleece. Once Tintin and the captain arrive in Istanbul, where the ship is anchored, they meet Mr. Karabine, a businessman who stubbornly insists on buying it even though it is in a dilapidated state.

Professor Calculus's friend develops a blue-skinned orange that can grow on any kind of land and survive harsh weather (in the manner of Lue Gim Gong) and therefore solve world hunger. The Professor and his friends, however, run afoul of gangsters who also covet the fruit. The adventure takes them from their home in Marlinspike Hall (Moulinsart), a fictional mansion that is presumably in Belgium, to Spain, where Calculus and another scientist are kidnapped.

When seven archaeologists find an ancient Inca temple, they become victims of an ancient curse. Back in Europe, one by one they fall into a deep sleep and only once a day, all at the same time, they wake up for a few minutes and experience hallucinations where the sinister living mummy of Rascar Capac appears.

Rascar Capac, the sinister creature featured on Hergé's album The Seven Crystal Balls (1948), has left its mark on many generations of readers. To draw it, the Belgian cartoonist was probably inspired by a mummy exhibited in the first pre-Columbian exhibition organized by the Brussels Cinquantenaire Museum in 1923. Two intrepid archaeologists embark on a fascinating journey to reconstruct the story of the mysterious mummy.